Small-scale Particle Clustering and Clustering Instability

  Description

    We predicted the effect of formation of small-scale inhomogeneities in spatial distribution of inertial particles advected by turbulent flow. This effect can be of great importance in various atmospheric and industrial flows, e.g., rain formation and fuel combustion in internal combustion engines. We developed a comprehensive theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution. The reason for the clustering instability is a combined effect of the particles inertia and a finite correlation time of the velocity field. The crucial parameter for the clustering instability is the size of the particles. The critical size of particles required for excitation of the clustering instability is estimated for a strong clustering, with a finite fraction of particles in clusters, associated with the growth of the mean absolute value of the particle number density and for a weak clustering associated with the growth of the second and higher moments. We introduced a new concept of compressibility of the turbulent diffusion tensor caused by a finite correlation time of an incompressible velocity field. In this model of the velocity field, the field of Lagrangian trajectories of particles is compressible. We suggested a mechanism of saturation of the clustering instability associated with the particles collisions in the clusters. An estimated nonlinear level of the saturation of the droplets number density in atmospheric clouds exceeds by the orders of magnitude their mean number density. The critical size of cloud droplets required for droplet cluster formation is of the order of 20 microns.

  References